(24+2x)(22+2x)=900

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Solution for (24+2x)(22+2x)=900 equation: 


Simplifying
(24 + 2x)(22 + 2x) = 900

Multiply (24 + 2x) * (22 + 2x)
(24(22 + 2x) + 2x * (22 + 2x)) = 900
((22 * 24 + 2x * 24) + 2x * (22 + 2x)) = 900
((528 + 48x) + 2x * (22 + 2x)) = 900
(528 + 48x + (22 * 2x + 2x * 2x)) = 900
(528 + 48x + (44x + 4x2)) = 900

Combine like terms: 48x + 44x = 92x
(528 + 92x + 4x2) = 900

Solving
528 + 92x + 4x2 = 900

Solving for variable 'x'.

Reorder the terms:
528 + -900 + 92x + 4x2 = 900 + -900

Combine like terms: 528 + -900 = -372
-372 + 92x + 4x2 = 900 + -900

Combine like terms: 900 + -900 = 0
-372 + 92x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-93 + 23x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-93 + 23x + x2)' equal to zero and attempt to solve:

Simplifying
-93 + 23x + x2 = 0

Solving
-93 + 23x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '93' to each side of the equation.
-93 + 23x + 93 + x2 = 0 + 93

Reorder the terms:
-93 + 93 + 23x + x2 = 0 + 93

Combine like terms: -93 + 93 = 0
0 + 23x + x2 = 0 + 93
23x + x2 = 0 + 93

Combine like terms: 0 + 93 = 93
23x + x2 = 93

The x term is 23x.  Take half its coefficient (11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
23x + 132.25 + x2 = 93 + 132.25

Reorder the terms:
132.25 + 23x + x2 = 93 + 132.25

Combine like terms: 93 + 132.25 = 225.25
132.25 + 23x + x2 = 225.25

Factor a perfect square on the left side:
(x + 11.5)(x + 11.5) = 225.25

Calculate the square root of the right side: 15.00833102

Break this problem into two subproblems by setting 
(x + 11.5) equal to 15.00833102 and -15.00833102.


Subproblem 1
x + 11.5 = 15.00833102

Simplifying
x + 11.5 = 15.00833102

Reorder the terms:
11.5 + x = 15.00833102

Solving
11.5 + x = 15.00833102

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-11.5' to each side of the equation.
11.5 + -11.5 + x = 15.00833102 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + x = 15.00833102 + -11.5
x = 15.00833102 + -11.5

Combine like terms: 15.00833102 + -11.5 = 3.50833102
x = 3.50833102

Simplifying
x = 3.50833102


Subproblem 2
x + 11.5 = -15.00833102

Simplifying
x + 11.5 = -15.00833102

Reorder the terms:
11.5 + x = -15.00833102

Solving
11.5 + x = -15.00833102

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-11.5' to each side of the equation.
11.5 + -11.5 + x = -15.00833102 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + x = -15.00833102 + -11.5
x = -15.00833102 + -11.5

Combine like terms: -15.00833102 + -11.5 = -26.50833102
x = -26.50833102

Simplifying
x = -26.50833102


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.50833102, -26.50833102}
Solution
x = {3.50833102, -26.50833102}

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